We describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto/visco-plastic models whose yield function incorporates the third stress invariant . The developments presented are based upon original results, proved in the paper, concerning the derivatives of eigenvalues and eigenprojectors of symmetric second-order tensors with respect to the tensor itself and upon an original algebra of fourth-order tensors obtained as second derivatives of isotropic scalar functions of a symmetric tensor argument . The analysis, initially referred to the small-strain case, is then extended to a formulation for the large deformation regime; for both cases we provide a derivation of the consistent tangent tensor which shows the analogy between the two formulations and the close relationship with the tangent tensors of the Lagrangian description of large-strain elastoplasticity.

A return map algorithm for general isotropic elasto/visco- plastic materials in principal space

VALOROSO, Nunziante;
2004

Abstract

We describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto/visco-plastic models whose yield function incorporates the third stress invariant . The developments presented are based upon original results, proved in the paper, concerning the derivatives of eigenvalues and eigenprojectors of symmetric second-order tensors with respect to the tensor itself and upon an original algebra of fourth-order tensors obtained as second derivatives of isotropic scalar functions of a symmetric tensor argument . The analysis, initially referred to the small-strain case, is then extended to a formulation for the large deformation regime; for both cases we provide a derivation of the consistent tangent tensor which shows the analogy between the two formulations and the close relationship with the tangent tensors of the Lagrangian description of large-strain elastoplasticity.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11367/26671
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